Powers of integer numbers as the sum of consecutive odd numbers

Authors

  • Marco Vásquez Instituto Tecnológico Andrés F. Córdova, Cañar, Ecuador

DOI:

https://doi.org/10.18537/mskn.04.02.05

Keywords:

natural number, odd, sum, power formula

Abstract

In this paper it is demonstrated that the power (p + q) of a natural number (n), can be derived as the sum of a series of consecutive odd numbers. The series of the summation is conditioned by a lower and upper boundary, being equal to half the difference plus 1, and respectively half the sum of the powers p and q of the natural number. The algorithm, notwithstanding its simplicity, offers some interesting opportunities in the applications of number theory to numerical analysis.

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References

Bazsó, A., H.M. Pintér, C. Srivastava, 2012. A refinement of Faulhaber’s theorem concerning sums of powers of natural numbers. Appl. Math. Lett., 25, 486-489.

De Santa Cruz, M.G., 1794. Dorado contador. Aritmética especulativa y práctica. Imprenta de don Benito Cano, Madrid, España, pp. 4-6.

Gaussianos.com, 2007. Sumando números impares. Descargado de http://gaussianos.com en 2011.

Knuth, D.E., 1993. Johann Faulhaber and sum of powers. Math. Comp., 61(203), 277-294.

Sen, S.K., H. Agarwal, 2006. 2n in scientific computation and beyond. Math. Comput. Modelling, 43, 658-672.

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Published

2013-12-25

How to Cite

Vásquez, M. (2013). Powers of integer numbers as the sum of consecutive odd numbers. Maskana, 4(2), 59–69. https://doi.org/10.18537/mskn.04.02.05

Issue

Vol. 4 No. 2 (2013)

Section

Research articles

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